Blender Model goes black only in Edit Mode
Your model has a lot of vertices, and that is perfectly fine.  The black lines indicate edges going between vertices on your model.  The vertices are hard to pick out at this distance, but when you zoom in on your model, the vertices (where the crossroads are) will be a little bit bigger.

Keep in mind that the point of Edit Mode is for you to select/deform/etc. the vertices, so it needs to display them.  While in Sculpt Mode or Object Mode, those vertices are not needed, so they are hidden, instead displaying the material of the object.

You can also look at this like the difference between Object Mode and Rendered Mode.  Both display the model, one using the OpenGL render (default for the 3D viewport), and the other is the Blender Internal render, which takes longer, but still displays your model, with different lighting calculations that give a more realistic result.